This workshop is an opportunity to consider the state of the art in
application of thermodynamics to mantle melting. This approach constructs and
calibrates Gibbs free energy models for relevant phases, enabling predictions of
equilibrium states including phase proportions, compositions, and some physical
properties. We will consider the achievements of this approach, its unfulfilled
promise, and its theoretical limits.

Under achievements, a body of work has applied the MELTS and pMELTS models to
upper mantle magmatism in ocean ridge, back-arc, intraplate, and subduction
environments. From 0-3 GPa pressure, models of multicomponent minerals and
silicate liquid appear good enough to recover most experimental results, to
provide an internally-consistent forward model from source peridotite through
melting to the observed volume and composition of magmas, to constrain the
potential temperature of source regions, to elucidate the role of water, and
more. There have been a few forays into integrating this approach with magma
dynamics at various scales.

Under promise, we expect near-future, improved versions that incorporate
carbon species, extend to substantially higher pressure, and account for
variable speciation in the melt to achieve higher fidelity. Calibration
strategies based on a flexible, evolving, community framework will liberate the
enterprise from the slow progress of models based on fixed,
internally-consistent datasets. Fully coupled, large-scale dynamical simulations
incorporating MELTS thermodynamics are practical and close to implementation.

Under limits, we must recall the limitations of the equilibrium assumptions
underlying thermodynamics. At some time and length scales these assumptions
break down. In a heterogeneous mantle containing species with widely divergent
mobility, there must be important roles for kinetics. Progress in incorporating
kinetics in major element models has been nearly nil and must be a major focus
of our efforts.